First-half goals from Armand Traore and captain Sean Morrison gave Warnock’s side a comfortable victory that leaves them just a point behind second-placed Aston Villa in the Championship.
Bolton never looked like managing a comeback at Cardiff City Stadium while Bruno Manga, Marko Grujic and Junior Hoilett came close to extending the home side’s lead.
Warnock said: “We were professional and we needed to be because it was always going to be difficult against a tough team like Bolton.
“We stayed strong in defence and talked about not giving an easy goal away because if you go 1-0 down it gives you a lot to do. We were tough at the back and scored two good goals.
“Armand’s goal was a good finish and Sean showed typical bravery for his header.”
On his Cardiff debut left back Traore found the bottom corner to open the scoring after Callum Paterson’s long throw fell loose inside the box.
Morrison then marked his 150th Bluebirds appearance by making it 2-0 with a close-range header at the second attempt.
“We have got to enjoy this moment,” said Warnock, whose Cardiff team are now fourth.
“We have a different game on Saturday because Middlesbrough will come here to win, but we are safe now and can’t get relegated. We are a good side and can get better.
“Kenneth Zohore had his best game for us for a while and Junior is like a bottle of fine wine.
“There were a lot of plusses and the hardest thing for me was telling Nathaniel Mendez-Laing and Greg Halford they couldn’t be on the bench.
“If that’s the biggest problem I’ve got between now and the end of the season, then I can deal with that.”
The visitors offered little as an attacking threat as Cardiff came out on top. Former Bluebird Adam le Fondre drove a second-half shot wide, but the Wanderers were always up against it.
Bolton manger Phil Parkinson said: “Cardiff played very well and we were second best. We didn’t do the basic things which we’re normally very good at.
“Cardiff can overpower sides and we had to stand strong against them. We did that at home, but we got overpowered here and we need to show some more fight and character in away games.
“We have to try and get a foothold in the game, but we didn’t do that. We showed some pride in the second half and made sure the scoreline remained respectable so we deserve some credit for that.
“We were resilient after the break to not concede again, but it was always going to be an uphill battle against a strong and powerful Cardiff side.
“For them to be in fourth alongside teams like Aston Villa with the resources they’ve got is full credit to Neil Warnock.”
Uwe Rosler was sacked by Fleetwood following a 3-0 reverse at Doncaster which condemned Town to a seventh straight defeat in all competitions.
Cambridge interim head coach Joe Dunne was pleased with how his side adapted to beat Grimsby 3-1.